The action by the US State Department is the latest salvo in a series of disputes between the rival powers and comes less than a month after US President Donald Trump met his Russian counterpart Vladimir Putin in Helsinki.
"In our view, these and earlier restrictions are absolutely unlawful and don't conform to worldwide law", Mr Peskov said.
Moscow would start to work on retaliatory measures "in the same spirit" as any United States restrictions, Russia's Foreign Ministry said.
The United States said Wednesday it was imposing new sanctions on Russian Federation over Moscow's involvement in the use of a "lethal" nerve agent in the attempted killing of a former spy in Britain.
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The U.S. made a similar determination in February when it found that North Korea used a chemical weapon to assassinate North Korean leader Kim Jong Un's half-brother at the airport in Kuala Lumpur, Malaysia, in 2017.
Image copyright Getty Images Image caption 2014: Protestors clash with authorities in Ukraine after the area of Crimea was annexed by Russia What different types of sanctions are there?
Police think the novichok was sprayed or smeared on their front doorknob with a perfume bottle.
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Speaking during a trip to Russia's far east, Mr Medvedev said: "I would not like to comment on talks about future sanctions, but I can say one thing: If some ban on banks' operations or on their use of one or another currency follows, it would be possible to clearly call it a declaration of economic war".
Department spokeswoman Heather Nauert said the administration had "complied with the law" and would continue to do so, but added: "We'd like to have a better relationship with the Russian government, recognizing that we have a lot of areas of mutual concern".
The sanctions came as an eagerly-watched contest for a previously safe Republican seat in the USA congress went to the wire, leading to speculation that voters were turning against Donald Trump and could punish the Republican Party at mid-term elections.
"Making a linking to these events (the British poisoning) is for us unacceptable and such restrictions like those passed by the American side earlier ... are absolutely illegal and do not correspond to worldwide law", said Kremlin spokesman Dmitry Peskov, according to a Reuters report. He insisted that Russia's financial system is strong enough to withstand shocks from the new penalties.
Zakharova described the new sanctions as an "unfriendly act" and accused the USA of trying to "demonize" Russian Federation. That could include the USA withdrawing support for global loans and US bank loans, blocking Russian airlines from landing in the USA, and suspending diplomatic relations.
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